Optimal boundary control of the wave equation: The finite-time turnpike phenomenon
- It is well-known that vibrating strings can be steered to a position of rest in finite time by suitably defined boundary control functions, if the time horizon is suffciently long. In optimal control problems, the desired terminal state is often
enforced by terminal conditions, that add an additional diffculty to the optimal control problem. In this paper we present an optimal control problem for the wave equation with a time-dependent weight in the objective function such that for a suffciently long time horizon, the optimal state reaches a position of rest in finite time without prescribing a terminal constraint. This situation can be seen as a realization of the finite-time turnpike phenomenon that has been studied recently in [1].